Research Team Seminars
Telescopers for Rational and Algebraic Functions via Residues
- Date : 19/07/2012
- Place : École polytechnique - Bâtiment Alan Turing, 1er étage salle 108
- Guest(s) : Shaoshi Chen, Symbolic Computation Group, North Carolina State University
- Organiser(s) : Algorithms Research team
We show that the problem of constructing telescopers for rational functions of m + 1 variables is equivalent to the problem of constructing telescopers for algebraic functions of m variables and we present a new algorithm to construct telescopers for algebraic functions of two variables. These considerations are based on analyzing the residues of the input. According to experiments, the resulting algorithm for rational functions of three variables is faster than known algorithms, at least in some examples of combinatorial interest. The algorithm for algebraic functions implies a new bound on the order of the telescopers. This is a joint work with Manuel Kauers (RISC) and Michael F. Singer (NCSU).